Simulating general relativity and non-commutative geometry by nonparaxial quantum fluids

We show that quantum fluids enable experimental analogs of relativistic orbital precession in the presence of non-paraxial effects. The analysis is performed by the hydrodynamic limit of the Schroedinger equation. The non-commutating variables in the phase-space produce a precession and an acceleration of the orbital motion. The precession of the orbit is formally identical to the famous orbital precession of the perihelion of Mercury used by Einstein to validate the corrections of general relativity to Newton’s theory. In our case, the corrections are due to the modified uncertainty principle. The results may enable novel relativistic analogs in the laboratory, also including sub Planckian phenomenology.

https://iopscience.iop.org/article/10.1088/1367-2630/ab5da8

Couplings between time and orbital angular momentum in propagation-invariant ultrafast vortices

In any form of wave propagation, strong spatiotemporal coupling appears when non-elementary, three-dimensional wave-packets are composed by superimposing pure plane waves, or spontaneously generated by light-matter interaction and nonlinear processes. Ultrashort pulses with orbital angular momentum (OAM), or ultrashort vortices, furnish a critical paradigm in which the analysis of the spatiotemporal coupling in the form of temporal-OAM coupling can be carried out accurately by analytical tools. By generalizing and unifying previously reported results, we show that universal and spatially heterogeneous space-time correlations occur in propagation-invariant temporal pulses carrying OAM. In regions with high intensity, the pulse duration has a lower bound fixed by the topological charge of the vortex and such that the duration must increase with the topological charge. In regions with low intensity in the vicinity of the vortex, a large blue-shift of the carrier oscillations and an increase of the number of them is predicted for strongly twisted beams. We think that these very general findings highlight the existence of a structural coupling between space and time, which is relevant at low photon numbers in quantum optics, and also in the highly nonlinear process as the high-harmonics generated with twisted beams. These results have also applications as multi-level classical and quantum free-space or satellite, communications, spectroscopy, and high-harmonic generation.

Miguel A. Porras and C. Conti in arXiv:1911.1222

Controlling rogue waves and soliton gases

Topological control of extreme waves

From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, transitions between extreme waves are allowed. However, these have never been experimentally observed because control strategies are still missing. We introduce the new concept of topological control based on the one-to-one correspondence between the number of wave packet oscillating phases and the genus of toroidal surfaces associated with the nonlinear Schrödinger equation solutions through Riemann theta functions. We demonstrate the concept experimentally by reporting observations of supervised transitions between waves with different genera. Considering the box problem in a focusing photorefractive medium, we tailor the time-dependent nonlinearity and dispersion to explore each region in the state diagram of the nonlinear wave propagation. Our result is the first realization of topological control of nonlinear waves. This new technique casts light on shock and rogue waves generation and can be extended to other nonlinear phenomena.

Nature Communications volume 10, Article number: 5090 (2019)

Docker, mpi, fftw, fftw-mpi

Docker enables to create containers for your program with all the libraries installed.

This avoids to reinstall all the libraries (say mpich, fftw…) to any user and in new systems

The user just needs to pull the container from a repository. For example nonlinearxwaves/base

I write C++ scientific computing programs with mpich, fftw-mpi and random numbers libraries (as sprng5), wich I need to run in both windows and linux systems. Docker simplifies a lot the deployment but also the development of the code.

nonlinearxwaves/base is a container with all of that

After installing Docker you run

docker login

Then you pull the docker image

docker pull nonlinearxwaves/base:0.1

You list the available images with

docker images -a

You identify the image id (in this example it is ec56f7250d5a)

REPOSITORY             TAG                 IMAGE ID            CREATED             SIZE
nonlinearxwaves/base 0.1 ec56f7250d5a 42 hours ago 1.13GB

You run the image with (you must replace the image id with your image id)

docker run -i -t ec56f7250d5a 

And you are in a shell with all the libraries installed and you may compile and run your mpi application in the usual way. In this image you will be the user “user”

user@2ff281ad4621:~$

The number 2ff281ad4621 is the container id that is now running (similar to a virtual machine)

This works with Windows and Linux (and also Mac, but I did not test)

You may also create your images with the Dockerfile

Is docker fast ? or is it better not to use a container? we will test …

emacs, auctex, Sumatra.pdf in Windows 10

On Windows 10 Pro

Install MiKTeX from https://miktex.org/

Download emacs zip file in the GNU mirror. I have chosen in http://mirror.lihnidos.org/GNU/ftp/gnu/emacs/windows/ the file in the folder emacs-26 http://mirror.lihnidos.org/GNU/ftp/gnu/emacs/windows/emacs-26/emacs-26.3-x86_64.zip

Unzip the emacs file in some folder for example Downloads folder, you will have a folder with name emacs-26.1-x86.4

Inside this emacs folder, click on runemacs

Now emacs is running, but you need to install auctex and Sumatra.pdf. You may create a shortcut to runemacs in the application bar by right clicking on it

To install auctex open emacs, then “M+x package-install auctex” and hit return

M+x package-install auctex

Sumatra.pdf enables to open multiple windows with the same pdf file. Acrobat blocks the compilation if the pdf is open.

Install Sumatra.pdf from https://www.sumatrapdfreader.org

Sumatra.pdf exe file will be in “C:\Program Files\SumatraPDF”

C:\Program Files\SumatraPDF

Now you need to configure emacs for using Sumatra.pdf, this is done by modifying the .emacs file

The .emacs file is the main configuration file for emacs

You find the .emacs file in the folder “C:\Users\<USER>\AppData\Roaming”

C:\Users\YourUserNameHere\AppData\Roaming

This is a hidden folder, you need to enable showing hidden folder in windows explorer (go to options in the folder menu)

Open .emacs and add the lines at the end of the file and save

(setq TeX-PDF-mode t)
(setq TeX-source-correlate-mode t)
(setq TeX-source-correlate-method 'synctex)
(setq TeX-view-program-list
'(("Sumatra PDF" ("\"C:/Program Files/SumatraPDF/SumatraPDF.exe\" -reuse-instance"
   (mode-io-correlate " -forward-search %b %n ") " %o"))))

(eval-after-load 'tex
 '(progn
   (assq-delete-all 'output-pdf TeX-view-program-selection)
   (add-to-list 'TeX-view-program-selection '(output-pdf "Sumatra PDF")))
 )
(server-start)

Now you are set to run auctex in emacs with forward search and Sumatra.pdf